Material science defines the structural properties of an object as the properties that describe the object's makeup independent from its shape. Adult human bone has a complex structure and can be described as a four-order hierarchy, arranged in decreasing size (Petersen, 1930). The first order, macrostructure (FIG. 1), comprises the structures corresponding to gross shape and differentiation between compact (or cortical) bone (FIG. 2) and spongy (cancellous or trabecular) bone (FIG. 3). Compact bone is present in the long bone shaft (or diaphysis). Spongy bone is present in the lower jaw (mandible), in the epiphysis of long bone shaft, and in flat and short bones. The second order (or microstructure) of compact bone includes lamellar systems (lamellae). Organized lamellae around vascular canals are referred to as osteons (harvesian systems) and disorganized lamellae among osteons are referred to as the interstitial bone. The second order also is comprised of related structures such as bone marrow (see e.g. Bloom and Fawcetts, 1986). The third order (or ultrastructure) of compact bone consists mainly of collagen bundles and hydroxyapatite crystallites; mucopolysaccarides amount to a small amout but may have a significant role. The fourth order of compact bone consists of molecular arrangements between organic and inorganic substances. For cancellous bone, the second order includes trabeculae, which comprise lamellar systems and related structures, e.g. bone marrow. The third and forth orders of cancellous bone are the same those described for compact bone.
The osteon comprises a haversian canal with concentrically arranged lamellae. Osteons of long bone are generally directed along the long bone axis. Osteonic lamellae are organized as consisting of an organic framework (mostly a collagen bundle) embedded in ground substances, such as proteins and water, and hydroxyapatite crystallites. The hydroxyapatite crystallites are oriented in directions analogous to those of the bundles. Osteons measure a few centimeters in length and are between 200 and 300 μm in diameter. The degree of osteon calcification (relative amount of hydroxyapatite crystallites) is variable from osteon to osteon as well as within osteons. These differences are proposed to be due to the process of bone renewal or remodeling. In this process, osteons are renewed continuously. Consequently, osteons at different degrees of calcification are always present in adult compact bone.
There is a spectrum of osteon types that refer to the arrangements of fiber bundle direction in the lamellae. Two osteon types, “longitudinal” and “alternate”, are representative of the two ends of the spectrum. Longitudinal osteons consist of bundles with a marked longitudinal spiral course. Alternate osteons consist of bundles with a marked longitudinal, oblique, and transversal course in successive lamellae (Frasca et al., 1977, Giraud-Guille, 1988, Ascenzi M.-G. et al., 2003). There are two types of lamellae, termed extinct (or longitudinal) and bright (or transverse or circularly-fibered) lamellae. Extinct (or dark) lamellae appear extinct whereas bright lamellae appear bright under a polarizing microscope when the microscope and osteon axes are aligned.
Compact bone consists of about 40% minerals, 40% collagen, and 20% fluids. The major internal spaces or discontinuities of compact bone include the vascular system, pits and cavities (lacunae), narrow channels (canaliculae), fine porosity, and spaces between the mineral phases. The major internal material discontinuities of compact bone (FIG. 5), in order of decreasing size, are:
Vascular system20-50μmLacunae4-6μmCanaliculae0.5-2μmFine porosity600-800ÅSpaces between mineral phases50-100Å
Cancellous bone consists of trabeculae, i.e. osseous structures with either a sheet-like or a rod-like configuration. These structures interlace to form a lattice-like or spongy biological structure (FIG. 3). For example, both types of trabeculae are present in the calcaneous; however, up to 3% of the rod-like configurations are tubular due to the vascular canal running through them. Therefore, they are similar to the harvesian system. In general, tubular trabeculae appear to have a relatively simple structure. Collagen fibrils run mostly parallel to the long axis of tubular trabeculae in the trabeculae outer portion and perpendicular in the inner portion. Although the true density of fully calcified cancellous bone is a little lower and the proteoglycan content a little greater than those of the fully calcified compact bone, the substantial difference between compact and cancellous bone resides in the porosity. The cancellous bone porosity, which ranges from 30% to more than 90%, is mainly due to the wide vascular and bone marrow intrabecular spaces. As is seen in compact bone, levels of calcification vary from trabecula to trabecula and within trabeculae.
The connections and orientations of trabeculae are found to have precise patterns, which are believed to relate to specific mechanical properties. The structure of the cancellous bone in the head and in the neck of the femur is usually given as an example of the correlation between the orientation of the trabeculae and the linear distribution of the principal forces during load bearing (stress trajectoral theory (Bell, 1956)). In general, such correlation between the orientation of the trabeculae and the linear distribution of the principal forces during load bearing is still under study because while in line with the mathematical calculations, the possible effect of muscle traction is complex (Koch, 1917; Rybicki et al., 1972). Nevertheless, there is a close relationship between the number and arrangement of trabeculae and the strength of cancellous bone (see e.g. Kleerekoper et al., 1985). This is evidenced by the age-induced loss of trabeculae (see e.g. Birkenhäger-Frenkel et al., 1988). Since this loss is rather selective (i.e. transverse trabeculae disappear more frequently than vertical ones in the central zone of the osteoporotic vertebral body; entire trabeculae totally disappear in elderly women; sharp fall in trabecular number is seen in elderly men), it is possible that cancellous bone contains some bundles of trabeculae whose main function is to resist mechanical forces while others have mainly a metabolic role.
The mechanical behavior of an object, or the response of an object to forces, of an object depends on the structure of the object. If the object is comprised of a hierarchical structure, the mechanical behavior of the object varies from order to order. That is, each order or level of the hierarchy responds to forces according to the structures and relationships within that order. Overall mechanical behavior of the object is ultimately determined by the mechanical properties of the different orders. Therefore, the mechanical properties of an object will vary with the hierarchical structure of the object. Bone is an example of an object where the mechanical behavior and mechanical properties are dependent upon this kind of hierarchical structure.
Mechanical properties of bone have been and are being investigated at various hierarchical levels through invasive (specimen isolation) and non-invasive testing. Osteonic trabecular lamellae, osteons, trabeculae, and macroscopic compact and cancellous bone samples have been and are the objects of such studies. Micromechanical results include Ascenzi A. and Bonucci, 1964, 1967; Ascenzi A. and Bonucci, 1968, 1972; Currey, 1969; Ascenzi A. et al., 1985, 1997, 1998; Hohling et al., 1990; Ascenzi A. et al., 1990, 1994; Marotti et al., 1994; Ziv et al., 1996; Ascenzi M.-G., 1999a, 1999b; Huja et al., 1999; Zysset et al., 1999; Ascenzi M.-G. et al., 2000. Macromechanical results include Hazama, 1956; Cook and Gordon, 1964; Carter and Hayes, 1976 and 1977; Carter et al., 1976 and 1981; Carter and Spengler, 1978; Hayes and Carter, 1979; Burr et al., 1988; Cater and Carter 1989; Jepsen and Davy, 1997.
Viscoelasticity
Material science regards viscoelasticity as a characteristic feature of polymer containing materials. Bone, like most biological materials, contains polymers. Viscoelastic properties depend on temperature and moisture content, which the work will hold constant at physiological level. In viscoelastic materials, some of the elastic energy generated by application of external forces is dissipated as heat. Such dissipated energy may contribute to the force driving the bone remodeling process (Levenston and Carter, 1998).
Studies of the mechanisms that generate bone viscoelasticity, that can shed light on the physico-chemical origin of Wolff's law and the properties of osteons, have not yet been conducted. However, osteon viscoelastic behavior could differ between longitudinal osteons and alternate osteons at the same degree of calcification (initial and final) and within each osteon type between initial and final stages of calcification. The only reported mechanical testing of whole osteons, isolated at their natural boundaries, is a preliminary non-systematic monotonic dynamic torsional loading (Frasca et al., 1981). It indicates structure and strain dependence of shear storage modulus in osteons of unspecified type and degree of calcification, and a linear viscous behavior up to strain values of 10−4. However, this model does not explain the behavior of the osteon structural components.
Even though numerous publications have addressed bone micromechanics in recent years, many biomechanical issues relating to bone are still not understood due to the lack of reliable or predictive models. The lack of inclusion of such micromechanical properties in current models of bone functions and behavior have severely limited their usefulness in predicting macromechanical properties. These properties include the bone behavior in response to external forces or identifying the requirements of bone reconstruction and prosthesis. However, the inclusion of these factors requires the development of methods and studies that may provide reliable and reproducible results.
There is a need in the art for realistic and meaningful models of bone behavior. To meet this need, the above-discussed parameters need to be investigated and resolved. The studies described herein provide surprising insights into the role of the underlying organizational arrangement of osteonic lamellar specimens in resisting applied loads. These findings are integrated into a novel and meaningful hierarchically based model of the mechanical behavior of macroscopic bone.
Such a model could provide clinicians with a tool to fundamentally improve the precision of their interventions.
The present invention describes a method to understand and predict the behavior of bone. The method includes a model of macroscopic bone which is constructed in terms of bone's hierarchical structural and mechanical properties and their interaction with forces acting on the macroscopic bone, including forces associated with the ordinary functioning of the body and forces applied clinically. The method can be applied to any bone structures, including human bone and the bones of vertebrates in general. The model applies to normal bone, and to pathological bone, when the pathology either does not alter the structural hierarchy, or when the alterations are characterized. The model is also applicable to fossilized bone.